Question

$9 {x}^{2} - \: 6 {b}^{2} x - ( {a}^{4} - {b}^{4} ) = 0$

Answer 1

hey Nikky 

9x² - 6b² x - (a⁴ - b⁴) = 0 

a = 9 

b = - 6b²

c = - (a⁴ - b⁴) 

D = b² - 4ac 

= (-6b²)² - 4 (9) ( - (a⁴ - b⁴) ) 

= 36b⁴ - 36 ( -a⁴ + b⁴) 

= 36b⁴ + 36a⁴ - 36b⁴

= 36a⁴

√D = √36a⁴ = 6a²

two roots are 

-b+√D/2a   and -b-√D/2a 

-(-6b²) + 6a²/ 2 x 9    and -(-6b²) - 6a² / 2 x 9 

6b² + 6a² / 18   and 6b² - 6a² / 18 

6(b² + a²) / 18  and 6(b² - a²) / 18 

b² + a² / 3   and b² - a² / 3 

^_^...